Local star-forming galaxies build up central mass concentration most actively near $M_{\ast}=10^{10}M_{\sun}$

The luminosity-weighted stellar age radial gradient $\nabla_{\rm age}$ describes the spatial distribution of stellar age within a galaxy. In this work, we consider SFGs with $\nabla_{\rm age}>0$ (younger central stellar age than the outer region) are undergoing/or recently underwent central mass build-up events. This method should be valid for detecting central mass build-up events involving recent central star formation. As mentioned above, bulge stars could also be originated from stellar radial migration or ex situ star formation (accreted from other galaxies). Such central mass build-up events are out of the scope of this work.

In the left panel of Figure 1, we show the SFR$-M_{\ast}$ plane for the 6916 galaxies selected in Section 2. Data points are color coded by $\nabla_{\rm age}$. In the SFR$-M_{\ast}$ plane, SFGs distribute along the star-formation main sequence (SFMS). To explore the $\nabla_{\rm age}$ distribution across the SFR$-M_{\ast}$ plane, we smooth the data using locally weighted regression method LOESS developed by Cleveland & Devlin (1988), with the PYTHON code released by Cappellari et al. (2013). LOESS is developed to uncover underlying mean trends by reducing observational errors and intrinsic scatters. We adopt a smoothing factor of $frac=0.1$, and a linear local approximation.

The right panel of Figure 1 shows the LOESS-smoothed version of the SFR$-M_{\ast}$ plane. As can be seen, at fixed $M_{\ast}$, galaxies with the highest SFRs tend to have positive $\nabla_{\rm age}$. Such galaxies are likely undergoing the compaction processes (Tacchella et al., 2016; Ellison et al., 2018), thus having enhanced SFRs compared to the SFMS ridge line. Along the ridge line of the SFMS, galaxies tend to have negative $\nabla_{\rm age}$. At log$(M_{\ast}/M_{\sun})>10.5$, SFGs have steep and negative $\nabla_{\rm age}$. This is consistent with the observation that massive SFGs typically harbor old bulge components (Pérez et al., 2013; Pan et al., 2015, 2016; Belfiore et al., 2017). Interestingly, SFGs near log$(M_{\ast}/M_{\sun})=10$ show shallower $\nabla_{\rm age}$ compared to those in the low-mass and high-mass regimes. In the low-SFR regime, galaxies generally have very shallow $\nabla_{\rm age}$. This is because the low-SFR regime is dominated by early-type galaxies, which typically exhibit very shallow age gradients (Parikh et al., 2021).

In this work, we focus our analysis on SFGs. SFGs are selected as those with log sSFR$>{-11.0}~{}\rm yr^{-1}$, where sSFR=${\rm SFR}/M_{\ast}$. 3590 SFGs are finally selected. In Figure 2, we show $\nabla_{\rm age}$ as a function of $M_{\ast}$ for the selected SFG sample. The mean value of $\nabla_{\rm age}$ is negative, which is around $-0.136~{}\rm log~{}Gyr{/R_{e}}$. This indicates that SFGs generally have older central stellar population than their outskirts, consistent with the ”inside-out” galaxy formation scenario (Wang et al., 2011; González Delgado et al., 2015; Pan et al., 2015).

To verify our SFG selection, we cross-match the MaNGA sample with the GALEX$-$SDSS$-$WISE Legacy Catalog (GSWLC, see Salim et al. 2016), which derive SFRs based on broad-band ultraviolet+infrared photometry. Of the 3590 MaNGA selected SFGs, 2579 ones have GSWLC counterparts. We find that 2471 ones ($\sim 95$%) also have log $\rm{sSFR_{GSWLC}>{-11.0}~{}yr^{-1}}$. This indicates that the SFG sample selected by $\rm{sSFR_{H_{\alpha}}}$ is almost all overlapped with that selected by $\rm{sSFR_{\rm GSWLC}}$.

We further divide the sample into stellar mass bins and investigate their $\nabla_{\rm age}$ distributions more specifically, with a bin size of $\Delta M_{\ast}=0.2~{}$dex. The result is shown in Figure 2. It is clear that the $\nabla_{\rm age}$ distribution exhibits a ”bump structure” near log$(M_{\ast}/M_{\sun})=10$. In this work, we consider SFGs with positive $\nabla_{\rm age}$ are undergoing/or have recently underwent central mass build-up processes, thus exhibiting younger central stellar ages than the outer regions. We then investigate the fraction of galaxies with positive $\nabla_{\rm age}$ (which we denote as $F_{\rm positive}$) in each stellar mass bin. To do this, the uncertainty of $\nabla_{\rm age}$ ($\sigma_{\nabla_{\rm age}}$) needs to take into account. We first construct the $\nabla_{\rm age}$ probability distribution function (PDF) for each SFG assuming a Gaussian form distribution centered at $\nabla_{\rm age}$, with a dispersion of $\sigma=\sigma_{\nabla_{\rm age}}$. With the constructed PDFs, we then perform bootstrapped resamplings to calculate $F_{\rm positive}$. We generate 500 realizations and derive the $F_{\rm positive}$ distribution at each stellar mass bin. The violin plot of the right panel of Figure 2 shows the result. As can be seen, the median $F_{\rm positive}$ is around 27% at log$(M_{\ast}/M_{\sun})=9.1$, while it rises up to $\sim$ 40% at log$(M_{\ast}/M_{\sun})\sim 10$ and then rapidly decreases, reaching its minimum value of $\sim 15\%$ near log$(M_{\ast}/M_{\sun})=11.0$. The peculiar distribution at log$(M_{\ast}/M_{\sun})=11.3$ may be of less statistical significance due to the small number of galaxies in this mass bin. The violin plot suggests that the excess of $F_{\rm positive}$ at log$(M_{\ast}/M_{\sun})\sim 10$ is of high significance.

The low fraction of SFGs with positive age gradients exhibits at log$(M_{\ast}/M_{\sun})>10.5$ is expected, since massive SFGs typically contain old bulge components (Pan et al., 2016; Belfiore et al., 2017). An interesting feature revealed in Figure 2 is that, low-mass SFGs seem to have a relatively low central mass build-up efficiency compared to those near log$(M_{\ast}/M_{\sun})=10$. We will come back to this issue in the discussion section.

Previous works reported that the radial gradients of many galactic properties are dependent upon galaxy morphologies (González Delgado et al., 2015; Li et al., 2018; Parikh et al., 2021). In this section, we investigate the dependence of $\nabla_{\rm age}$ on the morphologies of SFGs. In the left panel of Figure 3, we explore the distribution of $\nabla_{\rm age}$ across the $R_{\rm e}-M_{\ast}$ plane. At fixed $M_{\ast}$, SFGs with small $R_{\rm e}$ tend to have shallow or positive $\nabla_{\rm age}$. A similar trend is also exhibited across the $\Sigma_{*,1kpc}-M_{\ast}$ plane of SFGs (Woo & Ellison, 2019), where $\Sigma_{*,1kpc}$ is the stellar mass density in the central 1kpc region of a galaxy. The large symbols show the median sizes at fixed $M_{\ast}$, i.e, the size$-$mass relation. As can be seen, the slope of the size$-$mass relation is shallow at log$(M_{\ast}/M_{\sun})<10.0$ and becomes steepened and tighter toward the high mass end. In the right panel, we investigate the $\nabla_{\rm age}$ distribution across the $n-M_{\ast}$ plane. Data points with $n=6$ correspond to the largest value allowed in the Sérsic profile fitting (Blanton et al., 2005). Overall, SFGs with large $n$ tend to have shallow or positive $\nabla_{\rm age}$. At fixed $M_{\ast}$, $\nabla_{\rm age}$ is more strongly correlated with $R_{\rm e}$ than $n$. This may be due to the fact that a single Sérsic function is not a good parameterization of galaxy morphology (Tasca & White, 2011).

In Figure 4, we investigate the T-Type distributions for SFGs within two $\nabla_{\rm age}$ bins, $\nabla_{\rm age}>0$ and $\nabla_{\rm age}<-0.25$. As can be seen, SFGs with $\nabla_{\rm age}>0$ tend to have a broader T-Type distribution than those with $\nabla_{\rm age}<-0.25$. Also, SFGs with $\nabla_{\rm age}>0$ contain more fractions of galaxies with T-Type $\leq$ 3. This trend is particularly evident at log$(M_{\ast}/M_{\sun})<10.3$, which is consistent with the trend shown in the left panel of Figure 3. We perform a Kolmogorov-Smirnov (K-S) test to the T-Type distributions of the two samples. The small p-values of the K-S test suggest that these two distributions are statistically different. To conclude, at fixed $M_{\ast}$, SFGs with positive $\nabla_{\rm age}$ tend to have more centrally concentrated morphologies, consistent with the central mass build-up picture.

One may ask whether the MaNGA SFG sample is representative for the local SFGs in terms morphologies. To answer this question, we compare the $R_{\rm e}-M_{\ast}$ relation and the $f_{\rm n>2}-M_{\ast}$ relation of MaNGA SFGs with that of a local SFG comparison sample, where $f_{\rm n>2}$ is the fraction of SFGs with Sérsic index $n>2$. In the literature, galaxies with $n>2.5$ are considered to harbor prominent bulges, while those with $n<1.5$ are considered as bulgeless galaxies (Blanton et al., 2003; Bell et al., 2012). Inspecting the $n-M_{\ast}$ relation, we consider galaxies with $n>2$ have built a bulge component. The comparison SFG sample is selected from the NSA-Sloan catalog, which is the master photometric catalog of MaNGA Pipe3D. We first cross-match the NSA catalog with the GSWLC catalog to drive SFR measurements. Then we select SFGs with $b/a>0.4$ at $0.02<z<0.05$ as the comparison sample, with $\rm log~{}sSFR_{\rm GSWLC}>-11.0~{}yr^{-1}$. In this redshift range, the SDSS spectroscopic main galaxy sample is completed to $M_{*}\sim 10^{9}M_{\sun}$ (Schawinski et al., 2010). As mentioned before, the $\rm sSFR_{\rm GSWLC}$ selected SFGs are almost all overlapped with those selected by $\rm sSFR_{\rm H\alpha}$, thus this comparison should be physically meaningful. The comparison SFG sample contains $\sim 37000$ galaxies.

We show the result in Figure 5. As can be seen, the $R_{\rm e}-M_{\ast}$ relation of MaNGA SFGs is consistent with that of the NSA catalog at log$(M_{\ast}/M_{\sun})>10.0$. At log$(M_{\ast}/M_{\sun})<10.0$, MaNGA SFGs are biased against compact galaxies. On the one hand, this is partially due to the fact that we have removed the 19-fiber IFUs in the sample selection. We confirmed that when the 19-fiber IFUs are included, the discrepancy between the two samples in the $R_{\rm e}-M_{\ast}$ relation is reduced at log$(M_{\ast}/M_{\sun})<10.0$. On the other hand, this should be mainly due to the selection effect of MaNGA, because low-mass compact galaxies are difficult to spatially resolve in the MaNGA observation. Such a trend is confirmed by the $f_{\rm n>2}-M_{\ast}$ relation, where the $f_{\rm n>2}$ of MaNGA SFGs is lower than that of the NSA sample at log$(M_{\ast}/M_{\sun})<10.0$.

Figure 5 suggests that at fixed $M_{\ast}$, galaxies located in the high $R_{\rm e}$ region should be less affected by the selection effect of MaNGA. We thus divide the MaNGA SFG sample into two subsamples according to their $R_{\rm e}$, one with $R_{\rm e}>R_{\rm e,~{}median}$ and the other with $R_{\rm e}<R_{\rm e,~{}median}$. We show the $\nabla_{\rm age}-M_{\ast}$ relation for these two samples in Figure 6. As can be seen, the bump structure at log$(M_{\ast}/M_{\sun})\sim 10.0$ exhibits in both subsamples. Interestingly, it seems that the bump is more prominent in the $R_{\rm e}>R_{\rm e,~{}median}$ subsample, for which the result should be less affected by the MaNGA selection effect. To conclude, although the MaNGA SFG sample is biased against low-mass compact galaxies, our findings should not be significantly affected by this sample selection effect.

In this section, we first check the robustness of our analysis that based on luminosity-weighted age gradient. In the top left panel of Figure 7, we show the mass-weighted age gradient as a function of $M_{\ast}$. As can be seen, the mass-weighted age gradient exhibits no ”bump structure” near log$(M_{\ast}/M_{\sun})=10$, in stark contrast to Figure 2. The mean mass-weighted age gradient is also much shallower compared to the mean luminosity-weighted age gradient. This is because the mass-weighted quantities typically have narrower dynamical range than the luminosity-weighted quantities. In the top right panel, we show the 4000 Å break $D_{n}(4000)$ gradient as a function of $M_{\ast}$. $D_{n}(4000)$ is a commonly used stellar age indicator, which is sensitive to star formation activity on timescales of $\sim 1-2$ Gyr (Kauffmann et al., 2003; Wang et al., 2018). The $D_{n}(4000)$ gradient is flat at log$(M_{\ast}/M_{\sun})<10.2$ and turns negative toward the massive end, consistent with previous findings (Wang et al., 2018). Overall, the behavior of $D_{n}(4000)$ gradient follows that of the mass-weighted stellar age gradient, showing no excess of central mass build-up events near $M_{\ast}=10^{10}M_{\sun}$.

In the bottom left panel of Figure 7, we show the gradient of H$\alpha$ flux as a function of $M_{\ast}$. H$\alpha$ emission is sensitive to star formation activity on timescales of several Myr and is a traditional tracer of SFR. Thus, a very steep H$\alpha$ flux gradient indicates a high star formation concentration. Interestingly, the H$\alpha$ flux gradient steepens near log$(M_{\ast}/M_{\sun})=10.0$, which echoes the ”bump structure” we identify in Figure 2. In the bottom right panel of Figure 7, we show that SFGs with positive $\nabla_{\rm age}$ indeed have steepened H$\alpha$ flux gradient, indicative of more centrally concentrated star formation. To conclude, Figure 7 suggests that signs of central mass build-up events can be better detected using the radial gradients of star formation tracers on short timescales. In stead, mass-weighted stellar age and $D_{n}(4000)$ gradients are less sensitive to such events, possibly due to their narrow dynamical range.

At log$(M_{\ast}/M_{\sun})<9.5$, $\sim 80$% SFGs have $n<2$, i.e., the majority of low-mass SFGs have not built a central bulge component. In observation, low-mass SFGs are rich in neutral hydrogen (Hi) gas (Saintonge & Catinella, 2022). As shown in previous works, Hi gas plays an important role in the build-up of a disk component (Wang et al., 2011; Chen et al., 2020; Pan et al., 2021). With a high Hi gas fraction, disk rebuilding could be quit common for low-mass compact SFGs. In addition, major merger events, which are considered to be an important channel for bulge formation, are rare in this mass regime (Casteels et al., 2014; Rodriguez-Gomez et al., 2015). Finally, the bulge formation efficiency of low-mass galaxies can be suppressed by their high gas richness during merger events (Hopkins et al., 2009, 2010). These effects all potentially contribute to a low central mass build-up efficiency as seen in the low-mass regime.

At log$(M_{\ast}/M_{\sun})>10.5$, the majority of SFGs have built a bulge component (with $n>2$). For massive galaxies, major mergers are considered to play an important role in bulge formation (Hopkins et al., 2010). Recent studies showed that stellar migration may also contribute significantly to the build-up of central mass for Milky Way-mass galaxies (Boecker et al., 2023). The relative contribution of different mechanisms to the bulge formation of massive galaxies is a matter of intense debate. Regardless the detail formation mechanism, many bulges of massive SFGs show very low star formation activity, indicating that the central mass build-up process is largely completed, and the galaxies are on the path of star formation quenching (Belfiore et al., 2017).

SFGs with intermediate mass stand in a unique position in bulge formation. In the mass range of $9.5<{\rm log}(M_{\ast}/M_{\sun})<10.5$, neither ”mass quenching” is operated effectively (Peng et al., 2010), nor the SFGs are too rich in Hi gas. We indeed find evidence that SFGs near log$(M_{\ast}/M_{\sun})=10.0$ build up their central mass concentration most actively. Such a phenomenon is helpful to interpret the systematic morphological differences between low-mass and high-mass SFGs, as shown in Figure 5. We also note that our results are based on the low-redshift SFG sample. The bulge formation picture could be different at high redshift, as high-z galaxies exhibit more intense and clumpy star formation. In future work, it would be interesting to extend our study to higher redshifts to explore bulge formation across cosmic time.